MEASUREMENT OF POTENTIAL DIFFERENCE 249 



while a perfected form, designed at the National Physical Labora- 

 tory, and intended for work of high precision, is shown in Fig. 

 189, page 324. 



The arrangement of conductors is shown in Fig. 136. G,G f , 

 F,F' are the quadrants, usually made by cutting into four parts 

 a shallow metal box with its cover; for low potentials, the 

 diameter of the box is about 3 in., the depth about Yi in. The 

 quadrants are supported on insulating standards and are cross- 

 connected electrically by the wires b and e. 



The needle N, made of thin aluminum and of the form in- 

 dicated, is suspended within the box equally distant from the 

 top and the bottom. 



The directive moment is usually obtained by a torsion wire 

 or by a bifilar suspension. 



To deduce the formula for this electrometer, it will be as- 

 sumed that as the needle deflects, the rates of variation of the 

 capacities of the condensers formed by the needle and the 

 quadrants are uniform and independent of the angular dis- 

 placement of the needle, that the radial cuts dividing the quad- 

 rants are of negligible width and that only the five conductors, 

 F, F', G, G', N need be considered. 



The distribution of potentials will be assumed as indicated 

 in Fig. 136. Starting from the point a the fall of potential 

 to the second set of quadrants is d units. The further fall from 

 the second set of quadrants to the needle is V units. 



The needle N and the quadrants G, G' form a condenser which 

 is charged by a potential difference, V, while the needle and F, 

 F' form a condenser charged by a potential (V + d). The total 

 area of the needle under G and.G' is A. 



The energy of the condenser, considering both sides of the 

 needle, is 



A = 



so 



E = 



2 



2 



(5) 



If the needle be given a slight angular displacement, V being 



